Entropy of Hidden Markov Processes and Connections to Dynamical Systems
Papers from the Banff International Research Station Workshop

A collection of survey papers presenting important new results and focussing on the computation of the Shannon entropy rate.

Brian Marcus (Edited by), Karl Petersen (Edited by), Tsachy Weissman (Edited by)

9780521111133, Cambridge University Press

Paperback, published 26 May 2011

280 pages, 8 b/w illus.
22.6 x 15 x 1.5 cm, 0.4 kg

Hidden Markov processes (HMPs) are important objects of study in many areas of pure and applied mathematics, including information theory, probability theory, dynamical systems and statistical physics, with applications in electrical engineering, computer science and molecular biology. This collection of research and survey papers presents important new results and open problems, serving as a unifying gateway for researchers in these areas. Based on talks given at the Banff International Research Station Workshop, 2007, this volume addresses a central problem of the subject: computation of the Shannon entropy rate of an HMP. This is a key quantity in statistical physics and information theory, characterising the fundamental limit on compression and closely related to channel capacity, the limit on reliable communication. Also discussed, from a symbolic dynamics and thermodynamical viewpoint, is the problem of characterizing the mappings between dynamical systems which map Markov measures to Markov (or Gibbs) measures, and which allow for Markov lifts of Markov chains.

1. Hidden Markov processes in the context of symbolic dynamics Mark Boyle and Karl Petersen
2. On the preservation of Gibbsianess under symbol amalgamation Jean-René Chazottes and E. Ugalde
3. A note on a complex Hilbert metric with application to domain of analyticity for entropy rate of hidden Markov processes Guangyue Han, Brian Marcus and Yuval Peres
4. Bounds on the entropy rate of binary hidden Markov processes Erik Ordentlich and Tsachy Weissman
5. Entropy rate for hidden Markov chains with rare transitions Yuval Peres and Anthony Quas
6. The capacity of finite-state channels in the high-noise regime Henry Pfister
7. Computing entropy rates for hidden Markov processes Mark Pollicott
8. Factors of Gibbs measures for full shifts Mark Pollicott and Thomas Kempton
9. Thermodynamics of hidden Markov processes Evgeny Verbitskiy.

Subject Areas: Communications engineering / telecommunications [TJK], Maths for engineers [TBJ], Nonlinear science [PBWR], Probability & statistics [PBT]